On the Spectral Properties of the Landau Hamiltonian Perturbed by a moderately Decaying Magnetic Field

TL;DR

This paper investigates how the spectral properties of the Landau Hamiltonian are affected by a magnetic field with power-like decay, revealing the splitting of Landau levels and changes in spectral subspaces.

Contribution

It provides a detailed analysis of the spectral changes and Landau level splitting caused by a moderately decaying magnetic field perturbation.

Findings

Landau levels split under the perturbation

Spectral subspaces are altered by the decaying magnetic field

The spectral structure exhibits specific modifications due to the perturbation

Abstract

The Landau Hamiltonian, describing the behavior of a quantum particle in dimension 2 in a constant magnetic field, is perturbed by a magnetic field with power-like decay at infinity and a similar electric potential. We describe how the spectral subspaces change and how the Landau levels split under this perturbation.